COMPLETE MONOTONICITY OF TWO FUNCTIONS INVOLVING THE TRI- AND TETRA-GAMMA FUNCTIONS

被引：12

作者：

Zhao, Jiao-Lian ^{[1
]}

Guo, Bai-Ni ^{[2
]}

Qi, Feng ^{[2
]}

机构：

[1] Weinan Teachers Univ, Dept Math & Informat, Weinan City 714000, Shaanxi Provinc, Peoples R China

[2] Henan Polytech Univ, Sch Math & Informat, Jiaozuo City 454010, Henan Province, Peoples R China

来源：

PERIODICA MATHEMATICA HUNGARICA | 2012年 / 65卷 / 01期

关键词：

completely monotonic function; inequality; polygamma function; DIVIDED DIFFERENCES; POLYGAMMA FUNCTIONS; INEQUALITIES; DIGAMMA;

D O I：

10.1007/s10998-012-9562-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The psi function psi(x) is defined by psi(x) = Gamma'(x)/Gamma(x) and psi((i))(x), for i is an element of N, denote the polygamma functions, where Gamma(x) is the gamma function. In this paper, we prove that the functions [psi'(x)](2) + psi ''(x) - x(2)+12/12X(4)(x+1)(2) and x+12/12x(4)+(x+1) - {[psi'(x)(2) + psi ''(x)} are completely monotonic on (0, infinity).

引用

页码：147 / 155

页数：9

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